We've stayed at both the Elysée (where a friend is presently in residence and quite liking it) and the Lucerne. Both are excellent options.

I agree you don't really find European-style cafes much in NY, or most of the US, actually. Maybe San Francisco is the closest, but you can find something closer in more residential parts of Manhattan, the problem is there aren't usually hotels there.

I was down in the Lower East Side on one visit and wanted to find a place for late breakfast/brunch and stopped into Spiegel which is probably close enough to that concept. I think that's called the East Village, also.

This is it, you can see the style
https://www.theinfatuation.com/new-york/reviews/spiegel

I have a friend with a son who lives in the East Village and likes it okay, also. There are some hotels not far from there, like the Gatsby, the Ridge, the Ludlow, HOtel Indigo and Sixty. I don't know that they are any special anniversary type hotels. That area has some green space also with several parks around there. this is one
https://www.sixtyhotels.com/lower-east-side/
I wouldn't mind staying in that area, that hotel is around $300 for a suite during those dates.

I also like the area around the Flatiron building, a friend of mine really likes the Roger Smith HOtel which isn't too far from there near the library and Bryant Park. It isn't this super modern style, which I personally like, so if you do, that would be one idea. They have rooms for only $300 also plus a jr ste for only $320 which looks nice. That location is very convenient and I think enough things to walk to, plus the park. It's near the Waldorf Astoria.
https://www.rogersmith.com/



I do always stay in midtown though, as I mainly go to NY for Broadway and may even see two performances in one day on weekends. Then, I might also go to a museum, but those are mostly up that way, also, so I don't try to settle in much to a neighborhood feel. I don't know of any cafe-type place in midtown, at least not for breakfast. I can think of a couple places that are sort of similar to some European small restaurants for dinner.

The Jewel in Midtown near Rock Center is another thought.

I live in the East Village and we have just about ethnic type of restaurant. There is Lucien which a tad expensive. In the West Village is Cafe Loup, Tartine, and Buvette.